title: Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones.
abstract: Quantitative ultrasound has recently drawn significant interest in the monitoring of the bone healing process. Several research groups have studied ultrasound propagation in healing bones numerically, assuming callus to be a homogeneous and isotropic medium, thus neglecting the multiple scattering phenomena that occur due to the porous nature of callus. In this study, we model ultrasound wave propagation in healing long bones using an iterative effective medium approximation (IEMA), which has been shown to be significantly accurate for highly concentrated elastic mixtures. First, the effectiveness of IEMA in bone characterization is examined: (a) by comparing the theoretical phase velocities with experimental measurements in cancellous bone mimicking phantoms, and (b) by simulating wave propagation in complex healing bone geometries by using IEMA. The original material properties of cortical bone and callus were derived using serial scanning acoustic microscopy (SAM) images from previous animal studies. Guided wave analysis is performed for different healing stages and the results clearly indicate that IEMA predictions could provide supplementary information for bone assessment during the healing process. This methodology could potentially be applied in numerical studies dealing with wave propagation in composite media such as healing or osteoporotic bones in order to reduce the simulation time and simplify the study of complicated geometries with a significant porous nature.
authors.affiliation: Unit of Medical Technology and Intelligent Information Systems, Department of Materials Science and Engineering, University of Ioannina, GR 45110 Ioannina, Greece.
authors.forename: Vassiliki T
authors.initials: VT
authors.lastname: Potsika
authors.affiliation: Department of Mechanical Engineering and Aeronautics, University of Patras, GR 26500 Patras, Greece.
authors.forename: Konstantinos N
authors.initials: KN
authors.lastname: Grivas
authors.affiliation: Unit of Medical Technology and Intelligent Information Systems, Department of Materials Science and Engineering, University of Ioannina, GR 45110 Ioannina, Greece.
authors.forename: Vasilios C
authors.initials: VC
authors.lastname: Protopappas
authors.affiliation: Department of Mechanical Engineering and Aeronautics, University of Patras, GR 26500 Patras, Greece.
authors.forename: Maria G
authors.initials: MG
authors.lastname: Vavva
authors.affiliation: Julius Wolff Institute, Berlin-Brandenburg School for Regenerative Therapies, Charité-Universitätsmedizin Berlin, Augustenburger Platz 1, 13353 Berlin, Germany.
authors.forename: Kay
authors.initials: K
authors.lastname: Raum
authors.affiliation: Julius Wolff Institute, Berlin-Brandenburg School for Regenerative Therapies, Charité-Universitätsmedizin Berlin, Augustenburger Platz 1, 13353 Berlin, Germany.
authors.forename: Daniel
authors.initials: D
authors.lastname: Rohrbach
authors.affiliation: Department of Mechanical Engineering and Aeronautics, University of Patras, GR 26500 Patras, Greece.
authors.forename: Demosthenes
authors.initials: D
authors.lastname: Polyzos
authors.affiliation: Unit of Medical Technology and Intelligent Information Systems, Department of Materials Science and Engineering, University of Ioannina, GR 45110 Ioannina, Greece. Electronic address: fotiadis@cs.uoi.gr.
authors.forename: Dimitrios I
authors.initials: DI
authors.lastname: Fotiadis
mesh_terms: D001696:Biomechanical Phenomena; D002146:Bony Callus / Q000000981:diagnostic imaging / Q000502:physiology; D003198:Computer Simulation; D055119:Elastic Modulus; D017102:Fracture Healing / Q000502:physiology*; D050723:Fractures, Bone / Q000000981:diagnostic imaging* / Q000503:physiopathology; D006801:Humans; D033401:Microscopy, Acoustic; D008962:Models, Theoretical; D010024:Osteoporosis / Q000000981:diagnostic imaging / Q000503:physiopathology
keywords: Bone healing; Dispersion; Effective medium theory; Scanning acoustic microscopy; Ultrasound